Random beamforming (RBF) exploits multiuser diversity to increase the sum-rate capacity of MIMO broadcast channels. However, in the presence of spatial correlation between the downlink channels, multiuser diversity can not be exploited and the sum-rate suffers a signal to noise (SNR) hit. In this paper, we explore precoding techniques that minimize this hit. Basically, we derive an optimum and an approximate precoding matrix that minimizes the sum-rate hit of RBF. As a by product, we introduce a technique that evaluates the cumulative distribution function (CDF) of weighted norms of Gaussian random variables.